Darboux transformations and the algebra $\mathcal{D}(W)$
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866916582394953728 |
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| author | Parisi, Ignacio Bono Pacharoni, Inés |
| author_facet | Parisi, Ignacio Bono Pacharoni, Inés |
| contents | The problem of finding weight matrices $W(x)$ of size $N \times N$ such that the associated sequence of matrix-valued orthogonal polynomials are eigenfunctions of a second-order matrix differential operator is known as the Matrix Bochner Problem, and it is closely related to Darboux transformations of some differential operators.
This paper aims to study Darboux transformations between weight matrices and to establish a direct connection with the structure of the algebra $\mathcal D(W)$ of all differential operators that have a sequence of matrix-valued orthogonal polynomials with respect to $W$ as eigenfunctions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_16325 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Darboux transformations and the algebra $\mathcal{D}(W)$ Parisi, Ignacio Bono Pacharoni, Inés Classical Analysis and ODEs Operator Algebras 33C45, 42C05, 34L05, 34L10 The problem of finding weight matrices $W(x)$ of size $N \times N$ such that the associated sequence of matrix-valued orthogonal polynomials are eigenfunctions of a second-order matrix differential operator is known as the Matrix Bochner Problem, and it is closely related to Darboux transformations of some differential operators. This paper aims to study Darboux transformations between weight matrices and to establish a direct connection with the structure of the algebra $\mathcal D(W)$ of all differential operators that have a sequence of matrix-valued orthogonal polynomials with respect to $W$ as eigenfunctions. |
| title | Darboux transformations and the algebra $\mathcal{D}(W)$ |
| topic | Classical Analysis and ODEs Operator Algebras 33C45, 42C05, 34L05, 34L10 |
| url | https://arxiv.org/abs/2311.16325 |